The present invention relates to a scanning optical system such as a laser beam printer having no pitch irregularity and other scanning-associated problems.
A scanning optical system such as a laser beam printer which uses a semiconductor laser as a light source is shown schematically in FIG. 15; the system comprises a semiconductor 1 which emits a laser beam, a collimator lens 2 that produces substantially parallel rays of light from the beam emitted from the semiconductor laser 1, a deflector 3 such as a rotating polygonal mirror that deflects said rays of light, and a scanning lens system 4 that focuses the deflected rays to form a spot at a predetermined location on a scanning surface 5. In the following description, the direction in which scanning is performed on the scanning surface 5 is referred to as the principal scanning direction, and the direction normal to that scanning direction is referred to as the auxiliary scanning direction. If the diameter of the optical luminous flux is written as D, the focal distance of the scanning system 4 as f, and the wavelength as .lambda., then the diameter: EQU S=k.multidot..lambda..multidot.(f/D)
The scanning lens system 4 often employs an f.multidot..theta. lens so as to establish a linear relationship between the deflection rate and the scanning speed. The f.multidot..theta. lens is one that satisfies the relation: y=f.multidot..theta., wherein .theta. is the incident angle (i.e., the angle the incident beam forms with the optical axis of the lens) and y is the image height (i.e., the distance between the spot on the scanning surface 5 and the optical axis). This characteristic can be obtained by designing the scanning lens system so that it will have a negative value of distortion (Dist) expressed by: ##EQU1##
The semiconductor laser used as a light source radiates light in different modes as between the direction parallel to the junction surface (this direction is hereunder simply referred to as the parallel direction) and the direction perpendicular to that parallel direction (this direction is hereunder simply referred to as the normal direction). As shown in FIG. 16, the angle of spread of light in the parallel direction, .theta..sub.2, is smaller than the angle of spread in the normal direction, .theta..sub.1. In addition, light is radiated in the parallel direction from the semiconductor laser at a point more inward than the point where light is radiated in the normal direction, and this astigmatic difference will hereinafter be referred to as "astigmatism as" in FIG. 16.
Therefore, if the semiconductor laser having such characteristics is assembled into a scanning optical system that also includes a collimator lens, a deflector and a scanning lens system, light emitted from the laser will spread in different angles as between the parallel and normal directions. As a consequence, the diameter, D.sub.2, of the beam that emerges from the collimator lens in the parallel direction comes out to be different from the diameter, D.sub.1, of the beam emerging in the normal direction as follows: EQU D.sub.2 =fc sin (.theta..sub.2 /2)&lt;fc sin (.theta..sub.1 /2)=D.sub.1
(where fc is the focal distance of the collimator lens). This causes the diameter of the spot in the parallel direction to differ from the spot diameter in the normal direction as follows: EQU S.sub.2 =k.multidot..lambda.(f/D.sub.2)&gt;k.multidot..lambda.(f/D.sub.1)=S.sub.1
(where S.sub.2 is the spot diameter in the parallel direction, and S.sub.1 is the spot diameter in the normal direction). As a result, the spot formed on the scanning surface is by no means circular.
The astigmatism as inherent in the semiconductor laser causes another problem. The point at which an image is formed on the scanning surface by focusing through the scanning lens system 4 is offset in the optical axial direction as between the scanning direction and the direction normal to that direction (the latter direction is hereunder referred to as the auxiliary scanning direction), and the amount of this offset is given by: EQU .DELTA.=as.multidot.(f/fc).sup.2
where f is the focal distance of the scanning lens system, and fc is the focal distance of the collimator lens).
The first defect resulting from the use of a semiconductor laser as a light source, that is, the formation of a non-circular spot on the scanning surface, may be eliminated by the following beam shaping methods: (1) the aperture of the collimator lens 2 is reduced or a slit is provided, so that the light in the normal direction is rejected to provide light beams having the same diameter in both the parallel and normal directions; and (2) an afocal anamorphic optical system 10 is disposed between the collimator lens 2 and the deflector 3 as shown in FIG. 17, with a view to adjusting the diameter of light beam. The first method, however, reduces the energy efficiency of light while the second method requires a complicated optical system.
The second defect associated with the use of a semiconductor laser as a light source, that is, the offset of an image forming point in the optical axial direction that is caused by the astimatism as, may be eliminated by disposing a cylindrical lens 11 between the semiconductor laser and the collimator lens 2 or between the collimator lens 2 and the deflector 3, as shown in FIG. 18, so that the point at which laser light is emitted in the parallel direction is in apparent alignment with the point at which light is emitted in the normal direction. However, the cylinder lens 11 required in this method must have a large radius of curvature and is very difficult to manufacture.
A further problem results from the fact that the deflector 3 employs a rotating polygonal mirror or a hologram scanner; any error that is introduced by the unavoidable inclination of each of the surfaces of the polygonal mirror, or the error that exists between the elements of the hologram scanner will cause an error in the deflector surface in the auxiliary scanning direction, and this in turn causes uneveness in the scanning pitch.
Several methods have been proposed for solving the last-mentioned problem:
(1) As shown in FIG. 19, a first anamorphic optical system 13 that acts within a plane in the auxiliary scanning direction is disposed between the collimator lens 2 and the deflector 3 so as to form a line image on the deflector surface and, at the same time, a second anamorphic optical system 14 is added to the scanning lens system 4 or the scanning lens system 4 itself is designed to have an anamorphic configuration. By employing this arrangement, the deflector surface is rendered conjunctive with the scanning surface within a plane in the auxiliary scanning direction, so that any error that may be caused in the image point in the auxiliary scanning direction as a result of undesired inclination of the deflecting surface will be eliminated.
(2) As shown in FIG. 20, the first anamorphic optical system 13 acting within a plane in the auxiliary scanning direction is disposed in front of the deflector 3 but no line image is formed on the deflecting surface by that optical system, with the second anamorphic optical system 14 being added to the scanning lens system 4 or the scanning lens system 4 itself being designed to have an anamorphic configuration. This arrangement is intended to reduce the sensitivity of error in the image point to any unwanted inclination in the auxiliary scanning direction of the deflecting surface in the image forming optical system including the first anamorphic optical system 13.
Each of these techniques is disadvantageous in that:
(a) the first anamorphic optical system must be disposed in front of the deflector; and
(b) the optical system at the rear of the deflector provides such an increased positive refractive power in the auxiliary scanning direction that the curvature of field to be scanned is increased.
Examples of the scanning system employing the method (1) are shown in Japanese Patent Publication No. 28666/1977, and Unexamined Published Japanese Patent Application Nos. 144515/1982 and 93021/1983, while an example of the system using the method (2) is disclosed in Unexamined Published Japanese Patent Application No. 192920/1982. Each of the systems shown in these patents requires the use of a first anamorphic optical system having either a positive or a negative refractive power. In particular, the systems shown in Unexamined Published Japanese Patent Application Nos. 93021/1983 and 192920/1982 employ a cylindrical lens as the first anamorphic optical system, and in order to reduce the curvature of field, the length of the cylinder lens must be extended so that it can be disposed closed to the scanning surface.